Robust optimal policies for team Markov games

Abstract: In stochastic dynamic environments, team Markov games have emerged as a versatile paradigm for studying sequential decision-making problems of fully cooperative multi-agent systems. However, the optimality of the derived policies is usually sensitive to model parameters, which are typically unknown and required to be estimated from noisy data in practice. To mitigate the sensitivity of optimal policies to these uncertain parameters, we propose a robust model of team Markov games in this paper, where agents utilize robust optimization approaches to update strategies. This model extends team Markov games to the scenario of incomplete information and meanwhile provides an alternative solution concept of robust team optimality. To seek such a solution, we develop a robust iterative learning algorithm of team policies and prove its convergence. This algorithm, compared with robust dynamic programming, not only possesses a faster convergence rate, but also allows for using approximation calculations to alleviate the curse of dimensionality. Moreover, some numerical simulations are presented to demonstrate the effectiveness of the algorithm by generalizing the game model of sequential social dilemmas to uncertain scenarios.